Decomposing Non-Redundant Sharing by Complementation (SAS'99)

[Page last updated on "January 13, 2005, 15:31:42".]

Enea Zaffanella, Patricia M. Hill, Roberto Bagnara

Abstract

Complementation, the inverse of the reduced product operation, is a
relatively new technique for systematically finding minimal
decompositions of abstract domains. Filé and Ranzato advanced
the state of the art by introducing a simple method for computing a
complement. As an application, they considered the extraction by
complementation of the pair-sharing domain PS from the Jacobs
and Langen's set-sharing domain SH. However, since the result
of this operation was still SH, they concluded that PS
was too abstract for this. Here, we show that the source of this
difficulty lies not with PS but with SH and, more
precisely, with the redundant information contained in SH with
respect to ground-dependencies and pair-sharing. In fact, the
difficulties vanish if our non-redundant version of SH,
SH&rho;, is substituted for SH. To
establish the results for SH&rho;, we define a
general schema for subdomains of SH that includes
SH&rho; and Def as special cases. This
sheds new light on the structure of SH&rho; and
exposes a natural though unexpected connection between Def and
SH&rho;. Moreover, we substantiate the claim
that complementation alone is not sufficient to obtain truly
minimal decompositions of domains. The right solution to this
problem is to first remove redundancies by computing the
quotient of the domain with respect to the observable behavior, and
only then decompose it by complementation.